Name: UID: Section: 3 [40 points] A free water jet flows non-uniformly from a slot in the bottom of a circular pipe nozzle as shown in the figure. The flow entering the pipe at the flange has a uniform velocity, U = 6 m/s, across its circular cross-section (diameter D₁ = 0.05 m). The slot has dimensions of L = 0.25 m long by = 0.004 m wide, and it is known that the velocity varies linearly along the length of the slot, with the maximum velocity being twice the minimum velocity (Vmax = 2V/min). The density of water is p = 1000 kg/m³. The gravitational acceleration is g = 9.8 m/s². a) Determine the mass flowrate m exiting the nozzle and write an expression V(x) that describes the variation of the velocity across the exit slot. The origin of the x axis is at the upstream end of the slot, where V(x = 0) = Vmin, as shown in the figure. b) Given that the mass of the nozzle is M = 5 kg and the fluid volume contained in the nozzle is Q=0.001 m³, find the vertical component (y-direction) of the force F, required to hold the pipe in place. The y-axis is positive up. Patm U Di 11111 O Patm Vmin Vmax Cross-section view D1 Vmin Isotropic view Vmax